English
Related papers

Related papers: Inverse transmission problems for magnetic Schr\"o…

200 papers

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

Analysis of PDEs · Mathematics 2022-03-03 Mourad Bellassoued , Houssem Haddar , Amal Labidi

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…

Analysis of PDEs · Mathematics 2020-04-29 Jingzhi Li , Hongyu Liu , Shiqi Ma

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…

Analysis of PDEs · Mathematics 2020-02-24 Lauri Oksanen , Mikko Salo , Plamen Stefanov , Gunther Uhlmann

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…

Analysis of PDEs · Mathematics 2025-12-23 Yang Liu , Yixian Gao

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that the Cauchy data space (or Dirichlet-to-Neumann map $\mc{N}$) of the Schr\"odinger operator $\Delta +V$ with $V\in C^2(M_0)$ determines uniquely the potential…

Differential Geometry · Mathematics 2009-04-27 Colin Guillarmou , Leo Tzou

This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…

Analysis of PDEs · Mathematics 2012-09-06 Valter Pohjola

The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…

Spectral Theory · Mathematics 2018-05-22 Tuncay Aktosun , Vassilis G. Papanicolaou

We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…

Analysis of PDEs · Mathematics 2024-10-02 Mohamed Hamrouni , Moez Khenissi , Éric Soccorsi

In this paper, we establish positive results for two spectral inverse problems in the presence of a magnetic potential. Exploiting the principal wave trace invariants, we first observe that on closed Anosov manifolds with simple length…

Spectral Theory · Mathematics 2026-02-12 David dos Santos Ferreira , Benjamin Florentin

We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schr\"{o}dinger operator. This improves upon previous results of…

Analysis of PDEs · Mathematics 2014-02-19 Francis J. Chung

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…

Mathematical Physics · Physics 2007-05-23 M. Harmer

In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic…

Analysis of PDEs · Mathematics 2007-05-23 David Dos Santos Ferreira , Carlos Kenig , Johannes Sjoestrand , Gunther Uhlmann

A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…

Analysis of PDEs · Mathematics 2020-10-13 Samuel Cogar , Peter Monk

We study discrete Schroedinger operators with compactly supported potentials on the square lattice. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely…

Spectral Theory · Mathematics 2011-09-14 Hiroshi Isozaki , Evgeny Korotyaev

We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…

Mathematical Physics · Physics 2017-12-22 Hayk Asatryan , Werner Kirsch

Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…

Classical Analysis and ODEs · Mathematics 2023-12-25 Vladimir A. Zolotarev

In this paper we consider the inverse scattering problem for the Schr{\"o}dinger operator with short-range electric potential. We prove in dimension n $\geq$ 2 that the knowledge of the scattering operator determines the electric potential…

Analysis of PDEs · Mathematics 2018-09-07 Luc Robbiano , Mourad Bellassoued